Damping and Frequency Shift in Microscale Modified Couple Stress Thermoelastic Plate Resonators

In this paper, the vibrations of thin plate in modified couple stress thermoelastic medium by using Kirchhoff- Love plate theory has been investigated. The governing equations of motion and heat conduction equation for Lord Shulman (L-S) [1] theory are written with the help of Kirchhoff- Love plate theory. The thermoelastic damping of micro-beam resonators is analyzed by using the normal mode analysis. The solutions for the free vibrations of plates under clamped-simply supported (CS) and clamped-free (CF) conditions are obtained. The analytical expressions for thermoelastic damping of vibration and frequency shift are obtained for couple stress generalized thermoelastic and coupled thermoelastic plates. A computer algorithm has been constructed to obtain the numerical results. The thermoelastic damping and frequency shift with varying values of length and thickness are shown graphically in the absence and presence of couple stress for (i) clamped-simply supported, (ii) clamped-free boundary conditions. Some particular cases are also presented.

Keywords:

Modified couple stress theory , Thermoelasticity , Thermoelastic damping , Frequency shift